Applet showing a geometric method to find complex solutions to quadratic equations

Applet to show the geometric solutions to a quadratic equation:

In the geometric diagram, the right-angle path SP-O-B-C represents the quadratic equation, with positive coefficients, a, b, and c. The points, B and C, may be moved to show the effects of changes in the coefficients in both magnitude and sign. The line a' extending above the point B is equal to the line a. The red points x and x* show the positions of the two complex conjugate solutions in the x, y plane, where the x-axis is the horizontal blue line, with x = 0 at the point O and the y-axis is the vertical imaginary number axis. As the coefficients are moved, the solutions will move, and when the faint yellow circle intersects the x-axis, the solution will be real and will lie along the x-axis at the red points, x1 and x2.

If the mouse cursor is clicked on the applet and then the space bar is pressed, the applet will reset to its original position. The applet can be enlarged by clicking on the applet, pressing the return key, and dragging the lower right corner of the applet to any desired size.

References

Lill's method was first described in: Nouvelles Annales de Mathematiques, Series 2, Vol. 6, 1867, page 35.
The applet classes and attributes are provided through the The Geometry Applet by David E. Joyce at Clark University, Worcester, MA.